Do people here trust software wallets?

I always see the phrase "Not your keys, not your coins" thrown around, and I was wondering if keeping my coins in a software wallet is part of that.

While I do understand that having a hardware wallet is by far the most safe method of keeping your coins safe, does using software wallets (eg. I use Exodus) still count as being more safe than having the coins on exchanges?

And another question I have is why do people almost never mention these software wallets when it comes to being secure? Some people might not have the money to buy a hardware wallet, or might not have enough invested in crypto yet to find it worthwhile.